value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Matrices, problem faced by students

problem faced by students

Matlab, Help my matlab questions

Help my matlab questions

#title.automotive cruise control system., What are some of the interestingm...

What are some of the interestingmodern developments in cruise control systems that contrast with comparatively basic old systems

Determine series is convergent or divergent by root test, Find out if the f...

Find out if the following series is convergent or divergent. Solution There really is not very much to these problems another than calculating the limit and then usin

Concept, uses of maths concept

uses of maths concept

Find out general formula for tangent vector and unit vector, Find out the g...

Find out the general formula for the tangent vector and unit tangent vector to the curve specified by r → (t) = t 2 i → + 2 sin t j → + 2 cos t k → . Solution First,

Percentage, a washing machine costs $640 plus an installation charge of 7.5...

a washing machine costs $640 plus an installation charge of 7.5% what is the totalcost?

Project, report on shares and dovidend using newspaper

report on shares and dovidend using newspaper

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd